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Journal Article

Constraint qualifications and optimality conditions for optimization problems with cardinality constraints

Červinka Michal, Kanzow Ch., Schwartz A.

: Mathematical Programming vol.160, 1 (2016), p. 353-377

: GAP402/12/1309, GA ČR, GA15-00735S, GA ČR

: Cardinality constraints, Constraint qualifications, Optimality conditions, KKT conditions, Strongly stationary points

: 10.1007/s10107-016-0986-6

: http://library.utia.cas.cz/separaty/2016/MTR/cervinka-0461165.pdf

(eng): This paper considers optimization problems with cardinality constraints. Based on a recently introduced reformulation of this problem as a nonlinear program with continuous variables, we first define some problem-tailored constraint qualifications and then show how these constraint qualifications can be used to obtain suitable optimality conditions for cardinality constrained problems. Here, the (KKT-like) optimality conditions hold under much weaker assumptions than the corresponding result that is known for the somewhat related class of mathematical programs with complementarity constraints.

: BA